Quant Boosters  Kamal Lohia  Set 8

Q6) A group of worker was put on a job. From the second day onward, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. If no worker was withdrawn at any stage, the group would have finished the work in twothird time. How many worker were there in the group?
a. 2
b. 3
c. 5
d. 10
e. None of these

Q7) The price of a car rises by 30% while the sales come down by 20%. What is the percent change in total revenue? [CAT1996]
a. 4
b. 2
c. +4
d. +2

Q8) A is 50% as efficient as B. C does half the work done by A & B together. If C alone does the work in 40 days, then in how many days will A alone can do the work?
a. 30 days
b. 40 days
c. 45 days
d. 50 days
e. 60 days

Q9) A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
a. 12 days
b. 15 days
c. 16 days
d. 18 days

Q10) 2/5 of voters promise to vote for P and the rest promised to vote for Q. Of these, 15% of the voters went back of their promise to vote for P and 25% of the voters went back of their promise to vote for Q and P lost by 2 votes. Then total number of voters is
a. 100
b. 110
c. 90
d. 95

Q11) A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
a. Rs. 375
b. Rs. 400
c. Rs. 600
d. Rs. 800

Q12) The rate of inflation was 1000%. Then what will be the cost of an article, which cots 6 units of currency now, two years from now? [CAT1995]
a. 666
b. 660
c. 720
d. 726

Q13) A student took five papers in an examination, where the full marks were same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is [CAT2001]
a. 2
b. 3
c. 4
d. 5

Q14) I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what I paid. What percent of the total paid by me was for pens? [CAT1996]
a. 37.5%
b. 62.5%
c. 50%
d. None of these

Q15) Given the equation (5/2)x  b = (8/5)x + 142, find the smallest positive integer b such that the solution x is a positive integer.

Q16) Solve for x if (x  a  b)/c + (x  b  c)/a + (x  c  a)/b = 3 and ab + bc + ca ≠ 0.

Q17) Find the condition for 'a' such that equation ax  2y  3 + 5x + 9 = 0 has the solution (x, y) where x, y have same sign

Q18) Find the number of positive integer solutions of the equation 123x + 57y = 531.

Q19) Find all x which satisfy the equation x^4  12x^3 + 47x^2  60x = 0.

Q20) Given x  2 < 3, solve the equation x + 1 + x  3 + x  5 = 8.

Q21) Find real x such that xx  3x  4 = 0

Q22) For how many integers (m, n) whose absolute value is less than 7, the system of equations 3x + my  5 = 0 and x + ny  4 = 0 has no solution?

Q23) Assume the equation 2x² + x + a = 0 has the solution set A, and the equation 2x² + bx + 2 = 0 has the solution set B, and A ⋂ B = {1/2}, find A ⋃ B

Q24) Find real valued solutions (x, y, z) for the equation √(x) + √(y  1) + √(z  2) = (x + y + z)/2.

Q25) Solve the equation (x + 1)/(x + 4)  (x + 4)/(x + 1) + (x + 1)/(x  2)  (x  2)/(x + 1) = 2/3.